1. (c) University of Wisconsin, CS559 Spring 2002
Color Recap
The physical description of color is as a spectrum: the intensity of light at each wavelength
Humans have three types of cone – each responds differently to an incoming spectrum
Experiments show that humans can match all colors by combining three primary colors
The most common computer graphics primaries are Red (645.16nm), Green (526.32nm) and Blue (444.44nm)
01/29/02
(c) University of Wisconsin, CS559 Spring 2002

2. (c) University of Wisconsin, CS559 Spring 2002
Last Time
Digital Images
Spatial and Color resolution
Color
The physics and perception of color
Particularly: 3 types of cone, sensor response
01/29/02
(c) University of Wisconsin, CS559 Spring 2002

3. (c) University of Wisconsin, CS559 Spring 2002
Today
More on color
Trichromacy
Color matching
Color Spaces
01/29/02
(c) University of Wisconsin, CS559 Spring 2002

4. (c) University of Wisconsin, CS559 Spring 2002
Trichromacy
Experiment:
Show a target color beside a user controlled color
User has knobs that add primary sources to their color
Ask the user to match the colors
By experience, it is possible to match almost all colors using only three primary sources - the principle of trichromacy
Sometimes, have to add light to the target
In practical terms, this means that if you show someone the right amount of each primary, they will perceive the right color
This was how experimentalists knew there were 3 types of cones
01/29/02
(c) University of Wisconsin, CS559 Spring 2002

5. The Math of Trichromacy
Write primaries as R, G and B
We won’t precisely define them yet
Many colors can be represented as a mixture of R, G, B: M=rR + gG + bB (Additive matching)
Gives a color description system - two people who agree on R, G, B need only supply (r, g, b) to describe a color
Some colors can’t be matched like this, instead, write: M+rR=gG+bB (Subtractive matching)
Interpret this as (-r, g, b)
Problem for reproducing colors – you can’t suck light into a display device
01/29/02
(c) University of Wisconsin, CS559 Spring 2002

6. (c) University of Wisconsin, CS559 Spring 2002
Color Matching
Given a spectrum, how do we determine how much each of R, G and B to use to match it?
First step:
For a light of unit intensity at each wavelength, ask people to match it with R, G and B primaries
Result is three functions, r(), g() and b(), the RGB color matching functions
01/29/02
(c) University of Wisconsin, CS559 Spring 2002

7. The RGB Color Matching Functions
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(c) University of Wisconsin, CS559 Spring 2002

8. Computing the Matching
The spectrum function that we are trying to match, E(), gives the amount of energy at each wavelength
The RGB matching functions describe how much of each primary is needed to match one unit of energy at each wavelength
Hence, if the “color” due to E() is E, then the match is:
01/29/02
(c) University of Wisconsin, CS559 Spring 2002

9. (c) University of Wisconsin, CS559 Spring 2002
Color Spaces
The principle of trichromacy means that the colors displayable are all the linear combination of primaries
Taking linear combinations of R, G and B defines the RGB color space
the range of perceptible colors generated by adding some part each of R, G and B
If R, G and B correspond to a monitor’s phosphors (monitor RGB), then the space is the range of colors displayable on the monitor
01/29/02
(c) University of Wisconsin, CS559 Spring 2002

10. (c) University of Wisconsin, CS559 Spring 2002
RGB Color Space
Color Cube Program
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11. (c) University of Wisconsin, CS559 Spring 2002
Problems with RGB
Can only a small range of all the colors humans are capable of perceiving (particularly for monitor RGB)
Have you ever seen magenta on a monitor?
It isn’t easy for humans to say how much of RGB to use to make a given color
How much R, G and B is there in “brown”? (Answer: .64,.16, .16)
If you ever need to answer such questions, file rgb.txt under X11
Perceptually non-linear
two points a certain distance apart in one part of the space may be perceptually different
Two other points, the same distance apart in another part of the space, may be perceptually the same
01/29/02
(c) University of Wisconsin, CS559 Spring 2002

12. (c) University of Wisconsin, CS559 Spring 2002
CIE XYZ Color Space
Defined in 1931 to describe the full space of perceptible colors
Revisions now used by color professionals
Color matching functions are everywhere positive
Cannot produce the primaries – need negative light!
But, can still describe a color by its matching weights
Y component intended to correspond to intensity
Most frequently set x=X/(X+Y+Z) and y=Y(X+Y+Z)
x,y are coordinates on a constant brightness slice
01/29/02
(c) University of Wisconsin, CS559 Spring 2002

13. (c) University of Wisconsin, CS559 Spring 2002
CIE x, y
Note: This is a representation on a projector with limited range, so the right colors are not being displayed
01/29/02
(c) University of Wisconsin, CS559 Spring 2002

14. CIE Matching Functions
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(c) University of Wisconsin, CS559 Spring 2002

15. Qualitative features of CIE x, y
Linearity implies that colors obtainable by mixing lights with colors A, B lie on line segment with endpoints at A and B
Monochromatic colors (spectral colors) run along the “Spectral Locus”
Dominant wavelength = Spectral color that can be mixed with white to match
Purity = (distance from C to spectral locus)/(distance from white to spectral locus)
Wavelength and purity can be used to specify color.
Complementary colors=colors that can be mixed with C to get white
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(c) University of Wisconsin, CS559 Spring 2002

16. (c) University of Wisconsin, CS559 Spring 2002
Going from RGB to XYZ
These are linear color spaces, related by a linear transformation
Match each primary, for example:
Substitute and equate terms:
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(c) University of Wisconsin, CS559 Spring 2002

17. (c) University of Wisconsin, CS559 Spring 2002
Determining Gamuts
XYZ Gamut
Gamut: The range of colors that can be produced
Plot the matching coordinates for each primary
Region contained in triangle (3 primaries) is gamut
Really, it’s a 3D thing, with the color cube distorted and embedded in the XYZ gamut y
RGB Gamut G R B x
01/29/02
(c) University of Wisconsin, CS559 Spring 2002

18. More linear color spaces
Monitor RGB: primaries are monitor phosphor colors, primaries and color matching functions vary from monitor to monitor:
Almost all applications assume that RGB is the same as monitor RGB
YIQ: mainly used in television
Y is (approximately) intensity, I, Q are chromatic properties
Linear color space; hence there is a matrix that transforms XYZ coords to YIQ coords, and another to take RGB to YIQ
I and Q can be transmitted with low bandwidth
01/29/02
(c) University of Wisconsin, CS559 Spring 2002

19. (c) University of Wisconsin, CS559 Spring 2002
Munsell Color Space
Problems with linear spaces remain:
Hard to specify colors without resorting to matching functions
Perceptually non-uniform
Munsell: describes surfaces, rather than lights - less relevant for graphics
Surfaces must be viewed under fixed comparison light
01/29/02
(c) University of Wisconsin, CS559 Spring 2002

20. (c) University of Wisconsin, CS559 Spring 2002
Munsell color space
01/29/02
(c) University of Wisconsin, CS559 Spring 2002

21. HSV Color Space (Alvy Ray Smith, 1978)
Hue: the color family: red, yellow, blue…
Saturation: The purity of a color: white is totally unsaturated
Value: The intensity of a color: white is intense, black isn’t
Space looks like a cone
Parts of the cone can be mapped to RGB space
Not a linear space, so no linear transform to take RGB to HSV
But there is an algorithmic transform
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(c) University of Wisconsin, CS559 Spring 2002

22. (c) University of Wisconsin, CS559 Spring 2002
HSV Color Space
HSV Color Cone Program
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23. (c) University of Wisconsin, CS559 Spring 2002
Uniform Color Spaces
Color spaces in which distance in the space corresponds to perceptual “distance”
Only works for local distances
How far is red from green? Is it further than red from blue?
Use MacAdams ellipses to define perceptual distance
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(c) University of Wisconsin, CS559 Spring 2002

24. (c) University of Wisconsin, CS559 Spring 2002
MacAdam Ellipses
Scaled by a factor of 10 and shown on CIE xy color space
If you are shown two colors inside the same ellipse, you cannot tell them apart
Only a few ellipses are shown, but one can be defined for every point
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(c) University of Wisconsin, CS559 Spring 2002

25. (c) University of Wisconsin, CS559 Spring 2002
CIE u’v’ Space
CIE u’v’ is a non-linear color space where color differences are more uniform
Note that now ellipses look more like circles
The third coordinate is the original Z from XYZ
Violet
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(c) University of Wisconsin, CS559 Spring 2002

26. (c) University of Wisconsin, CS559 Spring 2002
Subtractive mixing
Inks subtract light from white, whereas phosphors glow
Common inks: Cyan=White−Red, Magenta=White−Green, Yellow=White−Blue
For example, to make a red mark, put down magenta and yellow, which removes the green and blue leaving red
For a good choice of inks, matching is linear:
C+M+Y=White-White=Black
C+M=White-Red-Green=Blue
Usually require CMY and Black, because colored inks are more expensive, and registration is hard
For good choice of inks, there is a linear transform between XYZ and CMY
01/29/02
(c) University of Wisconsin, CS559 Spring 2002